Dragonfly Wing - combining / cleaning up
I would suggest doing this by adjusting the Mean Radius in Edit Mode. This way you can make the outer parts thicker while still having them connected as a single mesh.

Mean Radius is a vertex attribute that is AFAIK exclusively for the Skin Modifier, to control the thickness of the resulting mesh.

With the vertices you want to adjust selected, click and drag-down to get both input fields selected. Then you can hold shift while moving the mouse to make fine adjustments, or type in a precise value.



And unless this is for an extreme close-up, you might want to just make a normal map out of this on a separate lower-poly mesh. That's a lot of geometry for something as small as a dragonfly wing. But this of course depends on the shot.

Update

Here is a .blend of just one wing for demonstration, based on the original file provided: